Q20. Write a proof in two-column form... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q20. (page 68)

Write a proof in two-column form for Exercise 19.
Exercise 19:Write a plan for a proof.
20. Given:鈭�3 is a supplement of鈭�1;
鈭�4 is a supplement of鈭�2.
Prove : $鈭� 3 鈮� 鈭� 4$ .

Short Answer

Expert verified

The proof in two column form is:

$鈭� 1 + 鈭� 3 = 180 掳$	Supplementary angles.
$鈭� 2 + 鈭� 4 = 180 掳$	Supplementary angles.
$鈭� 1 = 鈭� 2$	Vertically opposite angles.
$鈭� 1 + 鈭� 4 = 180 掳$	$鈭� 1 = 鈭� 2$
$鈭� 3 = 鈭� 4$	$鈭� 1 + 鈭� 4 = 鈭� 1 + 鈭� 3$

Step by step solution

Step 1. Observe the diagram.

鈭�3 is a supplement of鈭�1 and鈭�4 is a supplement of鈭�2.

The diagram is:

Step 2. Show the proof.

鈭�1 and鈭�3 are supplementary.

So, $鈭� 1 + 鈭� 3 = 180 掳$

鈭�2 and鈭�4 are supplementary.

So, $鈭� 2 + 鈭� 4 = 180 掳$

Also, 鈭�1 and 鈭�2 both are vertically opposite angle.

So, $鈭� 1 = 鈭� 2$ .

Then, $鈭� 1 + 鈭� 4 = 180 掳$ as $鈭� 1 = 鈭� 2$ .

Therefore,

$鈭� 3 = 鈭� 4$ since $鈭� 1 + 鈭� 4 = 鈭� 1 + 鈭� 3$ .

Step 3. State the conclusion.

The proof in two column form is:

$鈭� 1 + 鈭� 3 = 180 掳$	Supplementary angles.
$鈭� 2 + 鈭� 4 = 180 掳$	Supplementary angles.
$鈭� 1 = 鈭� 2$	Vertically opposite angles.
$鈭� 1 + 鈭� 4 = 180 掳$	$鈭� 1 = 鈭� 2$
$鈭� 3 = 鈭� 4$	$鈭� 1 + 鈭� 4 = 鈭� 1 + 鈭� 3$

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Statement	Reasons
1. $\overset{鈫�}{B X}$ is the bisector of $鈭� A B C$	1. ?
2. $鈭� A B X 鈮�$ ?, or $m 鈭� A B X =$ ?	2. ?
3. $m 鈭� A B X + m 鈭� X B C = m 鈭� A B C$	3. ?
4. $m 鈭� A B X + m 鈭� A B X = m 鈭� A B C$ , or $2 m 鈭� A B X = m 鈭� A B C$	4. ?
5. $m 鈭� A B X = \frac{1}{2} m 鈭� A B C$	5. ?
6. $m 鈭� X B C = \frac{1}{2} m 鈭� A B C$	6. Substitution Prop. (Steps ? and ?)

91影视

Write a proof in two-column form for Exercise 19.
Exercise 19:Write a plan for a proof.
20. Given:鈭�3 is a supplement of鈭�1;
鈭�4 is a supplement of鈭�2.
Prove : $鈭� 3 鈮� 鈭� 4$ .

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the proof.

Step 3. State the conclusion.

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91影视

Write a proof in two-column form for Exercise 19.Exercise 19:Write a plan for a proof.20. Given:鈭�3 is a supplement of鈭�1; 鈭�4 is a supplement of鈭�2.Prove : 鈭�3鈮�鈭�4.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the proof.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Write a proof in two-column form for Exercise 19.
Exercise 19:Write a plan for a proof.
20. Given:鈭�3 is a supplement of鈭�1;
鈭�4 is a supplement of鈭�2.
Prove : $鈭� 3 鈮� 鈭� 4$ .